The big idea
"Squashing the opposition" is when you bring up the objections the other side might have to your argument and then destroy them yourself with clever, well-constructed arguments. This way, you leave the other side with no ammunition. You do this even when you aren't in an actual debate; even when you are just writing a persuasive essay and there's nobody to argue against you, you should squash the opposition. This is because your reader may have some doubts about the point you are trying to make, and you want to get rid of them before they have a chance to get in the way.
Before you begin
Sit down and think about all the possible arguments that someone may have to go against what you have to say.
How to do it
Take the results of your brainstorming and look at them. Choose the counterarguments that you might best be able to demolish with some well-developed arguments of your own.
. . . .
Some examples:
It may be true that forcing public school students to wear uniforms might take away some of their individuality and freedom of expression, but that is only during actual school hours. They still have sixteen hours a day in which they can wear anything they want and express themselves to their hearts' content.
Some people might say that seeing violence on TV might prepare you for unexpected violence in your own life. These people think that seeing Jackie Chan defeat evildoers with kung fu will allow you to do the same thing the next time you're mugged. Nothing could be further from the truth; when was the last time you learned how to play a blistering guitar solo from watching one being played on MTV?